Nether Portal Blocks will sometimes get replaced with obsidian and air blocks, the frame can also get replaced with air blocks [13w24b]
(Warning all this only happens sometimes!)
To do this your self in the nether:
Step 1. Go to the nether.
Step 2. Made three more nether portals around the other portal in the nether.
Step 3. Leave world.
Step 4. Join world.
Enjoy!
To do this you self in the overworld:
Step 1. Go to the nether.
Step 2. Make a new nether portal long away from the other portal in the nether.
Step 3. Go back to the overworld through the new nether portal.
Enjoy!